A boundary integral formulation for predicting acoustic waves generated by large deformations of bodies

Abstract

This paper presents the application and assessment of a recently introduced boundary integral formulation for solving wave equations in domains bounded by porous or solid surfaces undergoing large deformations. Specifically, it is applied to predict acoustic waves generated by large-amplitude pulsations of a sphere immersed in an unbounded, quiescent, inviscid perfect gas. Fluid perturbations are expressed in terms of the velocity potential. The focus is on the assessment of the capability of the integral formulation to capture the effects induced by significant boundary deformations. To isolate these effects, fluid nonlinearities are neglected, as their contributions are given by field volume terms and fall outside the scope of this study. The numerical application of the boundary integral formulation is accomplished by a zero-th order boundary element method, complemented by a novel harmonic-balance approach for time integration. This innovative approach provides an efficient and robust solution method for handling periodic perturbation propagation phenomena. For a wide range of amplitudes and frequencies of sphere oscillation, the deformable-boundary integral formulation solving the linear wave equation for the velocity potential is validated against analytical linear solutions. In the case of large-amplitude, high-frequency pulsations the analytical solution, not available in the literature, is derived in this work under subsonic surface speed conditions. Numerical results highlight the multi-harmonic nature of the radiated acoustic field and provide an analysis of the boundary contributions associated with surface dynamic deformation. Successful applications to porous deforming spherical and wing-like shaped boundaries are also presented for the sake of completeness.